The Long Term Evolution (LTE) standard under consideration by the 3rd Generation Partnership Project (3GPP), the signal bandwidth may be configured from 1.4 MHz to 20 MHz. LTE uses orthogonal frequency-division multiple access (OFDMA) as the downlink channel. The bandwidth of the channel can be configured to 1.4 MHz, 3 MHz, 5 MHz, 10 MHz, 15 MHz and 20 MHz.
A cell search is a process by which a receiver acquires time and frequency synchronization with a cell and detects the physical layer cell ID of that cell. In LTE systems, this process is facilitated by the use of a primary sync signal (PSS) and secondary sync signal (SSS) (sometimes also referred to as the primary sync channel PSCH and the SSCH secondary sync channel respectively). Synchronization signals are specific sequences inserted into the last two OFDM symbols in the first slot of sub-frame zero and five (slots number 0 and 10). The PSS is carried on the PSS channel and the secondary sync signal is carried on the SSS channel. The primary synchronization signal is typically used for timing and frequency acquisition whereas the secondary signal is typically used to acquire the Cell ID and other cell-specific information. Both the PSSC and the SSSC are located in a 960 kHz band at the center of the signal and arrive in a symbol every 5 ms. There are 3 possibilities of PSS and 168 possibilities of SSS. Thus, there are 3*168=504 possibilities each of which is referred to as a Cell ID.
The Cell ID in the LTE system is composed of two parts, Nid1 and Nid2, where the Cell ID is calculated as Nid=Nid1*3+Nid2. The PSS (primary synchronization signal) corresponds to one of the three Nid2 codes, and the SSS (secondary synchronization signal) corresponds to one of the 168 Nid1 codes. The PSS symbol follows the SSS symbol in the LTE signal.
Synchronization (or acquisition) in an LTE system is a two-step procedure defined by the LTE standard specification. The first step is PSS detection to detect a time offset (frame timing) and Nid2, and the second step is SSS detection to select the Nid1 that has the maximum correlation energy.
Correlation is used to indicate how closely the two signals are related. For example, if there are two sequences of data X=[x1, x2, . . . , xL] and Y=[y1, y2, . . . , yL+M], wherein X is the reference sequence of L samples long, and Y is the received sequence of L+M samples long, to be correlated with X. The correlation between X and Y at time shifts k of Y is defined in Equation 1:
                                          ρ            ⁡                          (              k              )                                =                                    ∑                              i                =                1                            L                        ⁢                                                  ⁢                                          y                                  i                  +                  k                                            *                              conj                ⁡                                  (                                      x                    i                                    )                                                                    ,                  k          =          0                ,        …        ⁢                                  ,                  M          -          1.                                    [        1        ]            
In our example, X is the PSS or SSS reference signal sampled in the time domain, Y is the received signal of X through a communication channel that is characterized by a time delay j and amplitude a. Y has the form Y=[0,0, . . . , 0,ax1, ax2, . . . , axL,0, . . . , 0]. As PSS and SSS sequences are designed to have a good self-correlation property, the correlation output will appear as illustrated in FIG. 1, with a peak correlation at the delay j and low correlation elsewhere. Therefore, correlation is widely used to test if a known reference signal is present in the received signal at a specific delay.
In the case of the PSS and the SSS, the delay identifies the timing of the arrival of the PSS signal and permits the SSS signal to be located. Using the timing and the cell ID, the receiver synchronizes with the base station transmitter.
With respect to the detection of the SSS, the typical approach is to use only the SSS correlation to find the SSS. This approach discards information that may be obtained from the correlation of the PSS and is not always satisfactory under real-world conditions.
In a typical wireless communication system, the signal to be transmitted is upconverted to a carrier frequency prior to transmission. The receiver is expected to tune to the same carrier frequency for down-converting the signal to baseband prior to demodulation. However, under real-world conditions, the carrier frequency of the receiver may not be the same as the carrier frequency of the transmitter. When this happens, the received baseband signal, instead of being centered at DC (0 MHz), will be centered at a frequency offset from the desired center frequency.
Using existing systems, the acquisition detection may experience a loss of more than 2.0 dB when the carrier frequency offset is ±2.5 KHz. One possible cause of such loss may be the acquisition algorithm that is used.